Temperature

The thermodynamic temperature, symbol T, is a fundamental physical property and a base unit in the international system of units (SI). Up to 50% of all industrial observed parameters are temperature (Bernhard 2004), underlining the importance for all types of processes. The unit of the thermodynamic temperature is the Kelvin defined to be the 273.16th fraction of the triple point of water.

Constituents of matter perform translational, rotational and vibrational movements. Motility depends on chemical bondings determining the degrees of freedom for this high speed motion. Although this motion can just be detected with specialised equipment, the effect can be perceived as thermodynamic temperature. While the sum of absolute motions increases with higher temperatures, the mean motion velocity of all particles in a bulk quantity of matter is zero; or more precise equal to the velocity of the object. Matter whose constituents have no kinetic heat energy has the deepest possible temperature. This theoretical point is the absolute zero. 0K is equal to -273.15°C. On the microscopic level Brownian motion (Brown 1928) has early been related to temperature and observed to be more intensive with decreasing particle size (Smoluchowski 1906).

On the macroscopic level temperature determines the direction in which heat flows among objects being in thermal contact and varying in this property. The second law of thermodynamics states that heat flows from warmer to colder locations to reach equilibrium. Thermal transfer can be conducted by conduction, convection or thermal radiation. The latter one is not bound to transport by matter, but electromagnetic waves. Thus, heat can be transferred even under vacuum conditions (e.g. earth is heated by the sun).

Measuring temperature

Thermal radiation

A fundamental method to measure temperature makes use of the fact that any body with a thermodynamic temperature above absolute zero emits a temperature depending radiation. For an ideal black body the spectral distribution can be derived from Planck’s law:

M is the specific radiance power in W/(m2*µm), λ the wave length in meters and T the thermodynamic temperature of the black body in K. The constants are defined as c0= 299792458 m*s-1 (speed of light in vacuum), h=6.6260689633*10-34 J*s (Planck’s constant) and k=1.3806504*10−23 J*K-1 (Boltzmann constant). The spectrum and wave length of maximum intensity of radiation depends on temperature. This allows to measure radiation and to determine absolute thermodynamic temperature by identifying the wave length of maximum radiation intensity.

Contact measurement

Another common way to measure temperature is based on sensors being in thermal contact with the medium to be measured. In an ideal case sensor and medium are in an thermal equilibrium. The temperature of a system can be measured by a property of the respective sensor system E(ϑ), that drifts with temperature. This property can be used as proxy (e.g. temperature depended change in electrical voltage, resistance or volume). If variation of E is linear within a given range of ϑ the system can be described by a simple linear equation:

To determine a and b requires two fixed points ϑ1 and ϑ2. At E(ϑ1) and E(ϑ2) temperatures are arbitrarily defined. Thus, a and b become:

For comparing such measurements the fixed points need to be calibrated to a reproducible scale. Ancient temperature scales often use the melting and boiling point of water as fixed points, to which arbitrary values are assigned. Temperatures different from the two points can then be inter- or extrapolated.

Ancient calibration of liquid thermometers made to a large extent use of this concept. Such devices consist of a bulb enclosing a liquid and a capillary connected to the bulb. Heating or cooling causes expansion or contraction of the liquid. Amplified by the narrower bore the meniscus in the capillary varies with temperature. To exclude barometric effects the capillary is normally sealed and the volume above the meniscus is often evacuated or filled with nitrogen.

Anyhow precise measurement of thermodynamic temperature is prone to a couple of problems. The coefficient of volumetric thermal expansion is often not completely linear throughout the entire range of the thermometer scale. Two thermometers calibrated to two points, but using different liquids can show different temperatures far from the calibration points. The temperature difference between the medium, measured by the bulb, and the surrounding temperature of the capillary may also have an impact on the measurement. To be precise the capillary needs to be narrow, so that minor changes in temperature can be conceived. In contrast the capillary becomes very long for covering a certain range, restraining manageability. Thus, highly precise liquid thermometers just cover small ranges.

Temperature scales

Classical temperature scales

Measuring temperature in comparable ways requires calibrated and reproducible scales. Therefore, several scales were established, known as the classical temperature scales. While some of them are still in use, nowadays relevance of others lays in the comparability with historic measurements. Original definitions of classical temperature scales are often based on liquid thermometers with two or three calibration points. Between these calibration points the scale was interpolated or extrapolated beyond. With increasing progress in measuring technology multiple fixed points were defined and scales defined by equations. This is reflected in the promulgation of the international temperature scales.

Newton scale

Around 1700 the English natural scientist Isaac Newton devised one of the first temperature scales. Unsatisfying approaches with up to 20 fixed points showed that these points were hard to reproduce (e.g. cold air or glowing charcoal). For a revised scale he used a linseed oil thermometer. For melting ice Newton used the value 0 and the value 33 was defined to be the boiling point of water. Although this scale is disused today it is still important in historical contexts. The unit increment of the Newton scale was the degree Newton (°N).

Rømer scale

In 1701 the Danish astronomer Ole Christensen Rømer proposed a temperature scale using two fixed points. The first was given by the freezing point of a defined salt-ice mixture and defined to be 0. The second point was the boiling point of water to which a value of 60 was assigned. Rømer found that at approximately 1/8th of his scale the freezing point of water was located. For practical reasons it became a further calibration point at 7.5 degree on his scale. Today the Rømer scale is a disused temperature scale, with importance to historical temperature measurement. The unit increment of the Rømer scale is the degree Rømer (°Rø).

Fahrenheit scale

After a contact with Rømer the german physicist Daniel Gabriel Fahrenheit developed a temperature scale with three fixed points for better calibration. Presumably in winter 1708/09 he determined the zero point of his scale as the deepest temperature he could produce with a cooling bath of a salmiac-ice mixture. By this he avoided negative every day temperatures. Around 1714 the second and third point was determined. The ice point of water was assigned to be 32 degree Fahrenheit and the body temperature of a sound human being with 96 degree Fahrenheit.By this he made use of a 12-based scale, common at this time. The advantage was an 8-fold increased precision by increased number of divisions and a scale being often divisible without remainders. The unit increment of the Fahrenheit scale is the degree Fahrenheit (°F).

Celsius scale

In 1742 the Swedish astronomer Anders Celsius introduced a scale that used the freezing and boiling point of water as fixed points. Using a liquid thermometer the position of the meniscus was named zero when the bulb was dipped into boiling water and the melting/freezing point of water was named one hundred. Between these two points temperatures were interpolated on a scale of 100 equal parts. For practical reasons these values were swapped around 1850 and the scale referred to as centigrade scale. With the adaptation as an international proposed scale the name of the scale was defined as Celsius scale. The unit increment of the Celsius scale is the degree Celsius (°C).

Réaumur scale

Based on a liquid thermometer with a mixture of 80% alcohol and 20% water the French scientist René Antoine Ferchault de Réaumur introduced another scale in 1731. The zero point of the scale was the ice point of water and the boiling point was determined to be 80. The unit increment of the Réamur scale is the degree Réaumur (°Ré, but also °R).

Kelvin scale

In 1848 William Thomson (later Lord Kelvin) proposed a new temperature scale with an absolute zero as the scale’s null point (Thomson 1848). He included knowledge derived from the works of Carnot and Gay-Lussac on thermodynamics and the relation between volume, temperature and pressure of gases. By this Thomson determined the absolute zero with an accuracy of a few tenth of one degree centigrade and extended this concept from gases to all matter. Prior to the 13thConférence Générale des Poids et Mesures in 1967 the unit increment of the Kelvin scale was the degree Kelvin (°K). In 1967/68 it was renamed to merely Kelvin (K), dropping the term degree and the unit Kelvin was defined to be the 1/273.16th of the triple point of water given in degree Centigrade.

Rankine scale

Similar to the scale of Kelvin the Scottish scientist and engineer William John Macquorn Rankine introduced 1859 a scale with an absolute zero. Instead of using the centigrade scale he made use of the unit proposed by Fahrenheit. The Rankine thermodynamic scale is still in use in some countries abiding to the Fahrenheit scale. The unit increment of the Rankine scale is the degree Rankine (°Ra or sometimes °R and thus might be confused with the Réaumur sclae). The amount of unit increment is one degree Rankine (°Ra), which is equal to that of the Fahrenheit scale.

International temperature scales

The problem of scale precision has been discovered early and brought forth a couple of approaches and international agreements on measuring temperature. The Kelvin or Celsius scale is defined by absolute zero (0 K, -273.15 °C) and the triple point of water (273.16 K, 0.01 °C). Anyhow, interpolation is impractical for the precise measurements of temperatures far away from these points. With increasing possibilities applications demanded higher resolution to measure thermodynamic temperatures with precisions higher than <0.0001 °C. This was achieved by creating scales with several fixed points. For traceability most of the calibration points for thermodynamic temperature scales are based on phase transitions of chemical elements. Especially melting and freezing points are used.

To harmonise temperature measurements the International Committee of Weights and Measures (BIPM, Bureau International des Poids et Mesures, www.bipm.org) promulgates standards to calibrate equipment for measuring temperature. Since 1889 the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) of the BIPM meets in irregular terms of 4 to 6 years to discuss recent issues on the International System of Units (SI). From the CGPM several temperature scales were introduced, meeting present technical improvements.

These scales are designed to represent the absolute thermodynamic temperature as close as possible, within currently possible ranges. Differences among scales are mainly based on discarding and including new fixed points. A good compendium is given by Preston-Thomas (1990), given here in an amended summary:

Temperature scale of 1913

The 5th CPGM adopted the first international temperature scale in 1913. Constants for measurements by platinum resistance thermometers were specified and proposed that above the upper limit of these the scale were enhanced by using the optical pyrometers.

International Temperature Scale of 1927

The seventh CGPM adopted the International Temperature Scale of 1927 (ITS-27). At this time several differing national scales existed and disallowed direct comparisons. Furthermore the ITS-27 tried to meet concerns in difficulties of the direct realisation of thermodynamic temperatures by gas thermometry.

The scale was formulated to allow measurements to be approximated to thermodynamic temperatures as close as could be determined at that time and to make measurements reproducible. Between the oxygen boiling point and gold freezing point it was based upon a number of reproducible temperatures, or fixed points, to which numerical values were assigned, and two standard interpolating instruments. Each of these interpolating instruments was calibrated at several of the fixed points, this giving the constants for the interpolating formula in the appropriate temperature range. Aplatinum resistance thermometer was used for the lower part and a platinum rhodium/platinum thermocouple for temperatures above 660°C. Above the gold freezing point, temperatures were defined in terms of the Wien radiation law: in practice, this invariably resulted in the selection of an optical pyrometer as the realizing instrument.

International Temperature Scale of 1948

The ninth CGPM adopted the International Temperature Scale of 1948 (ITS-48). Changes from the ITS-27 were: the lower limit of the platinum resistance thermometer range was changed from -190 °C to the defined oxygen boiling point of -182.97 °C, and the junction of the platinum resistance thermometer range and the thermocouple range became the measured antimony freezing point (about 630 °C) in place of 660 °C; the silver freezing point was defined as being 960.8 °C instead of 960.5 °C; the gold freezing point replaced the gold melting point (1063 °C).

The Planck radiation law replaced the Wien law. The value assigned to the second radiation constant became 1.438*10-2 m*K in place of 1.432*10-2 m*K; the permitted ranges for the constants of the interpolation formulae for the standard resistance thermometer and thermocouple were modified; the limitation on λTfor optical pyrometry (λT< 3*10-3 m*K) was changed to the requirement that “visible” radiation be used. Based on the not finally verified results of 1930 it was also defined that the triple point of water was equivalent to 273.16 K (0.01 °C)

International Practical Temperature Scale of 1948 (Amended edition of 1960)

The eleventh CGPM (in 1960) adopted the International Practical Temperature Scale of 1948 (IPTS-48) in an amended version (IPTS48, amended version 1960). In addition to the introduction of the word “Practical”, the modifications to the ITS-48 were: the triple point of water, defined as being 0.01°C, replaced the melting point of ice as the calibration point in this region; the freezing point of zinc, defined as being 419.505°C, became a preferred alternative to the sulphur boiling point (444.6°C) as a calibration point. The permitted ranges for the constants of the interpolation formulae for the standard resistance thermometer and the thermocouple were further modified. The restriction to “visible” radiation for optical pyrometry was removed. Inasmuch as the numerical values of temperature on the IPTS-48 were the same as on the ITS-48, the former was not a revision of the scale of 1948 but merely an amended form.

International Practical Temperature Scale of 1968 (IPTS-68)

In 1968 the International Committee of Weights and Measures promulgated the International Practical Temperature Scale of 1968 (IPTS-68), as empowered by the thirteenth General Conference of 1967-1968. The IPTS-68 incorporated very extensive changes from the IPTS-48, including numerical changes, designed to bring it more nearly in accord with thermodynamic temperatures that were sufficiently large to be apparent to many users.

Other changes were: the lower limit of the scale was extended down to 13.81 K; at even lower temperatures (0.5 K to 5.2 K), the use of two helium vapour pressure scales was recommended; six new defining fixed points were introduced - the triple point of equilibrium hydrogen (13.81 K), an intermediate equilibrium hydrogen point (17.042 K), the normal boiling point of equilibrium hydrogen (20.28 K), the boiling point of neon (27.102 K), the triple point of oxygen (54.361 K), and the freezing point of tin (231.9681 °C) which became a permitted alternative to the boiling point of water; the boiling point of sulphur was deleted; the values assigned to four fixed points were changed - the boiling point of oxygen (90.188 K), the freezing point of zinc (419.58 °C), the freezing point of silver (961.93 °C), and the freezing point of gold (1064.43 °C); the interpolating formulae or the resistance thermometer range became much more complex; the value assigned to the second radiation constantc2became 1,4388 * 10-2 m*K; the permitted ranges of the constants for the interpolation formulae for the resistance thermometer and thermocouple were again modified.

International Practical Temperature Scale of 1969 (Amended edition of 1975)

The fifteenth General Conference in 1975 adopted the International Practical Temperature Scale of 1968, amended edition of 1975. As was the case for the IPTS-48 with respect to the ITS-48, the IPTS-68(75) introduced no numerical changes. Most of the extensive textural changes were intended only to clarify and simplify its use. More substantive changes were: the oxygen point was defined as the condensation point rather than the boiling point; the triple point of argon (83.798 K) was introduced as a permitted alternative to the condensation point of oxygen; new values of the isotopic composition of naturally occurring neon were adopted; the recommendation to use values of T given by the 1958 4He and 1962 3He vapour-pressure scales was rescinded.

1976 Provisional 0.5 K to 30 K Temperature Scale (EPT-76)

The 1976 provisional 0.5K to 30 K temperature scale was introduced to meet two important requirements. These were to provide means of substantially reducing the errors (with respect to corresponding thermodynamic values) below 27 K that were then known to exist in the IPTS-68 and throughout the temperature ranges of the 4He and 3He vapour pressure scales of 1958 and 1962 respectively. The second point was to bridge the gap between 5.2 K and 13.81 K in which there had not previously been an international scale. Other objectives in devising the ETP-76 were “that it should be thermodynamically smooth, that it should be continuous with the IPTS-68 at 27.l K, and that is should agree with thermodynamic temperature T as closely as these two conditions allow”. In contrast with the IPTS-68, and to ensure its rapid adoption, several methods of realizing the ETP-76 were approved. These included: using a thermodynamic interpolation instrument and one or more of eleven assigned reference points; taking differences from the IPTS-68 above 13.81 K; taking differences from helium vapour pressure scales below 5K; and taking differences from certain well-established laboratory scales. Because there was a certain “lack of internal consistency” it was admitted that “slight ambiguities between realizations” might be introduced. However the advantages gained by adopting the EPT-76 as a working scale until such time as the IPTS-68 should be revised and extended were considered to outweigh the disadvantages.

International Temperature Scale of 1990 (ITS-90)

The International Temperature Scale of 1990 (ITS-90) defines 14 fixed points for calibration between 13.8033 K (-259.3467 °C) and 1357.77 K (1084.62 °C). Additionally four overlapping equations are specified to calculate temperature from vapour-pressure to temperature relations of helium isotopes in the range of 0.65K (-272.50 °C) to 5 K (-268.15 °C). ITS-90 replaced the older International Practical Temperature Scale of 1968 (IPTS-68). To measure the entire range many thermometer designs are required, including helium vapour, helium gas, platinum resistance and radiation thermometers.

The triple point of water depends on its isotopic composition. Thus, the 23rd meeting of the CGPM (CGPM 2007) defined that the definition of the Kelvin refers to a specific composition of referenced material known as the Vienna Standard Mean Ocean Water (VSMOW, de Laeter et al 2003). The triple point of the VSMOW is the only point known with absolute precision as the Celsius and Kelvin scale are fixed on this point by international agreement.

References

Brown R. (1828): A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Philosophical Magazine 4:161-173.

Comptes Rendus de la 9e CGPM (1948), 1949, 55; Triple point of water; thermodynamic scale with a single fixed point; unit of quantity of heat (joule)